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If a coin and a die are tossed find the probability of obtaining a head and at least 3 on the die ✅ Mới nhất

Kinh Nghiệm về If a coin and a die are tossed find the probability of obtaining a head and least 3 on the die Mới Nhất

Hoàng Gia Trọng Phúc đang tìm kiếm từ khóa If a coin and a die are tossed find the probability of obtaining a head and least 3 on the die được Update vào lúc : 2022-09-26 09:50:34 . Với phương châm chia sẻ Mẹo về trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi tham khảo nội dung bài viết vẫn ko hiểu thì hoàn toàn có thể lại phản hồi ở cuối bài để Ad lý giải và hướng dẫn lại nha.

Here we will learn how to find the probability of tossing three coins.

Nội dung chính
    What is the probability of getting least 3 head?What is the probability of getting 3 on a dice and head on coin?What is the probability of getting a tail on the coin and least a 3 on the die?What is the probability of getting a 3 after tossing the rolling die?

Let us take the experiment of tossing three coins simultaneously:

When we toss three coins simultaneously then the possible of outcomes are: (HHH) or (HHT) or (HTH) or (THH) or (HTT) or (THT) or (TTH) or (TTT) respectively; where H is denoted for head and T is denoted for tail.

Therefore, total numbers of outcome are 23 = 8

The above explanation will help us to solve the problems on finding the probability of tossing three coins.

Worked-out problems on probability involving tossing or throwing or flipping three coins:

1. When 3 coins are tossed randomly 250 times and it is found that three heads appeared 70 times, two heads appeared 55 times, one head appeared 75 times and no head appeared 50 times. 

If three coins are tossed simultaneously random, find the probability of: 

(i) getting three heads,

(ii) getting two heads,

(iii) getting one head,

(iv) getting no head

Solution:

Total number of trials = 250.

Number of times three heads appeared = 70.

Number of times two heads appeared = 55.

Number of times one head appeared = 75.

Number of times no head appeared = 50.

In a random toss of 3 coins, let E1, E2, E3 and E4 be the events of getting three heads, two heads, one head and 0 head respectively. Then,

(i) getting three heads

P(getting three heads) = P(E1)

      Number of times three heads appeared
=                   Total number of trials         

= 70/250

= 0.28

(ii) getting two heads

P(getting two heads) = P(E2)

      Number of times two heads appeared
=                 Total number of trials         

= 55/250

= 0.22

(iii) getting one head

P(getting one head) = P(E3)

      Number of times one head appeared
=                 Total number of trials        

= 75/250

= 0.30

(iv) getting no head

P(getting no head) = P(E4)

      Number of times on head appeared
=                 Total number of trials      

= 50/250

= 0.20

Note:

In tossing 3 coins simultaneously, the only possible outcomes are E1, E2, E3, E4 and P(E1) + P(E2) + P(E3) + P(E4)

= (0.28 + 0.22 + 0.30 + 0.20) 

If a coin and a die are tossed find the probability of obtaining a head and at least 3 on the die

2. When 3 unbiased coins are tossed once.

What is the probability of:

(i) getting all heads

(ii) getting two heads

(iii) getting one head

(iv) getting least 1 head

(v) getting least 2 heads

(vi) getting atmost 2 heads

Solution:

In tossing three coins, the sample space is given by

S = HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

And, therefore, n(S) = 8.

(i) getting all heads

Let E1 = sự kiện of getting all heads. Then,
E1 = HHH
and, therefore, n(E1) = 1.
Therefore, P(getting all heads) = P(E1) = n(E1)/n(S) = 1/8.

(ii) getting two heads

Let E2 = sự kiện of getting 2 heads. Then,
E2 = HHT, HTH, THH
and, therefore, n(E2) = 3.
Therefore, P(getting 2 heads) = P(E2) = n(E2)/n(S) = 3/8.

(iii) getting one head

Let E3 = sự kiện of getting 1 head. Then,
E3 = HTT, THT, TTH and, therefore,
n(E3) = 3.
Therefore, P(getting 1 head) = P(E3) = n(E3)/n(S) = 3/8.

(iv) getting least 1 head

Let E4 = sự kiện of getting least 1 head. Then,
E4 = HTT, THT, TTH, HHT, HTH, THH, HHH
and, therefore, n(E4) = 7.
Therefore, P(getting least 1 head) = P(E4) = n(E4)/n(S) = 7/8.

(v) getting least 2 heads

Let E5 = sự kiện of getting least 2 heads. Then,
E5 = HHT, HTH, THH, HHH
and, therefore, n(E5) = 4.
Therefore, P(getting least 2 heads) = P(E5) = n(E5)/n(S) = 4/8 = 1/2.

(vi) getting atmost 2 heads

Let E6 = sự kiện of getting atmost 2 heads. Then,
E6 = HHT, HTH, HTT, THH, THT, TTH, TTT
and, therefore, n(E6) = 7.
Therefore, P(getting atmost 2 heads) = P(E6) = n(E6)/n(S) = 7/8

3. Three coins are tossed simultaneously 250 times and the outcomes are recorded as given below.

Outcomes

3 heads

2 heads

1 head

 No head

Total

Frequencies

48

64

100

38

250

If the three coins are again tossed simultaneously random, find the probability of getting 

(i) 1 head

(ii) 2 heads and 1 tail

(iii) All tails

Solution:

(i) Total number of trials = 250.

Number of times 1 head appears = 100.

Therefore, the probability of getting 1 head

                                                   = (fractextrmFrequency of Favourable TrialstextrmTotal Number of Trials)

                                                   = (fractextrmNumber of Times 1 Head AppearstextrmTotal Number of Trials)

                                                   = (frac100250)

                                                   = (frac25)

(ii) Total number of trials = 250.

Number of times 2 heads and 1 tail appears = 64.

[Since, three coins are tossed. So, when there are 2 heads, there will be 1 tail also].

Therefore, the probability of getting 2 heads and 1 tail

                                         = (fractextrmNumber of Times 2 Heads and 1 Trial appearstextrmTotal Number of Trials)

                                         = (frac64250)

                                         = (frac32125)

(iii) Total number of trials = 250.

Number of times all tails appear, that is, no head appears = 38.

Therefore, the probability of getting all tails

                                                   = (fractextrmNumber of Times No Head AppearstextrmTotal Number of Trials)

                                                   = (frac38250)

                                                   = (frac19125).

These examples will help us to solve different types of problems based on probability of tossing three coins.

Probability

Probability

Random Experiments

Experimental Probability

Events in Probability

Empirical Probability

Coin Toss Probability

Probability of Tossing Two Coins

Probability of Tossing Three Coins

Complimentary Events

Mutually Exclusive Events

Mutually Non-Exclusive Events

Conditional Probability

Theoretical Probability

Odds and Probability

Playing Cards Probability

Probability and Playing Cards

Probability for Rolling Two Dice

Solved Probability Problems

Probability for Rolling Three Dice

9th Grade Math

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What is the probability of getting least 3 head?

N=3: To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin. Thus there are only 4 outcomes which have three heads. The probability is 4/16 = 1/4.

What is the probability of getting 3 on a dice and head on coin?

Answer: If you flip a coin 3 times the probability of getting 3 heads is 0.125.

What is the probability of getting a tail on the coin and least a 3 on the die?

1 Answer. The possibility of rolling a 3 on a fair die and getting tails on a coil is 112 .

What is the probability of getting a 3 after tossing the rolling die?

Probability of getting 3 in a die = (number of favorable sự kiện) / (total number of sự kiện). P(3) = (1)/(6). Hence, the probability of getting 3 after tossing a rolling die is 1/6 or 0.167. Tải thêm tài liệu liên quan đến nội dung bài viết If a coin and a die are tossed find the probability of obtaining a head and least 3 on the die

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