A marksman has an accuracy of 0.6, that is he can hit the target 6 out of 10 times. If he shoots at the target four times, what is the probability that he has hit the target at least once?
Solution
The probability that he misses the target all four times is given by $$0.4 ^ 4$$. Hence, the probability that he has hit the target is $$1 - 0.4 ^4$$ = 0.9744.
Question 3
If an unbiased coin is tossed 5 times, what is the probability of getting heads at least 3 times?
Solution
The probability of getting 0 heads is $$\frac{1}{32}$$. The probability of getting exactly one head = $$ ^5 C _1 (0.5)(0.5^4) = \frac{5}{32}$$ and two heads = $$ ^5 C _2 *(0.5^2)(0.5^3)= \frac{10}{32}$$.
Hence probability of getting 3 or more heads = $$1-\frac{1}{32}-\frac{5}{32}-\frac{10}{32} = \frac{1}{2}$$
A class of 10 people including 7 men and 3 women were taking the class photo by standing in a single line. What is the probability that at most 2 of the 3 women stand adjacent to each other?
Solution
Let E be an event that all three of them stand next to each other.
Considering the women as one unit we can arrange people in 8!3! ways.
Hence P(E)= 8!3!/10! = 1/15.
Hence the probability that at most two of them stand next to each other is 1-1/15= 14/15.
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