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How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
Let us assume that, man tosses the coin n times. Thus, n tosses are the Bernoulli trials
∴ Probability of getting head at the toss of the coin
Let us assume,
∴
It is given in the question that,
Probability of getting at least one head >
∴
1 – P (x = 0) > 0.9
(i)
Hence, the minimum value of n satisfying the given inequality = 4
∴ The man have to toss the coin 4 or more times
Suppose we have four boxes A, B, C and D containing coloured marbles as given below:
Box | Marble colour | ||
Red | White | Black | |
A | 1 | 6 | 3 |
B | 6 | 2 | 2 |
C | 8 | 1 | 1 |
D | 0 | 6 | 4 |
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?