Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
3 heads = 23 times
2 heads = 72 times
1 head = 77 times
No head = 28 times
From the above,compute the probability of the following:
i) at least 2 head
ii)3 tails
iii)at most one head
iv)at least 1 tail
Answers
Answer:
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
3 heads = 23 times
2 heads = 72 times
1 head = 77 times
No head = 28 times
From the above,compute the probability of the following:
i) at least 2 head
ii)3 tails
iii)at most one head
iv)at least 1 tail
Given:
Three coins are tossed simultaneously 200 times
3 heads = 23 times
2 heads = 72 times
1 head = 77 times
No head = 28 times
To find:
i) Probability of at least 2 head
ii) Probability of 3 tails
iii) Probability of at most one head
iv) Probability of at least 1 tail
Solution:
i) Number of times at least two heads coming up = 72 + 23
= 95
Probability of at least two heads = number of times at least 2 heads come up/The total number of times the coins were tossed
= 95/200
= 19/40
Hence, the probability of at least two heads coming up is 19/40.
ii) Number of times 3 tails = 28
Probability of 3 tails = number of times 3 tails/The total number of times the coins were tossed
= 28/200
= 19/100
Hence, the probability of 3 tails coming up is 19/100.
iii) Number of times at most one head = 77 + 28
= 105
Probability of at most one head = number of times at most one head/The total number of times the coins were tossed
= 105/200
= 21/40
Hence, the probability of at most one head is 21/40.
iv) Number of times at least one tail = 72 +77 +28
= 177
Probability of at least one tail = number of times at least one tail/The total number of times the coins were tossed
= 177/200
Hence, the probability of at least one tail is 177/200.