Four fair coins are tossed simultaneously. Given that at least two heads appear, what is the probability that exactly three heads occur?
4/11
With 4 coins, the total number of outcomes is \(2^4 = 16\).
The number of ways to get exactly \(k\) heads is \(\binom{4}{k}\): for 2 heads it is \(\binom{4}{2} = 6\), for 3 heads \(\binom{4}{3} = 4\), and for 4 heads \(\binom{4}{4} = 1\).
So the event "at least two heads" has \(6 + 4 + 1 = 11\) outcomes.
Using conditional probability, \(P(\text{exactly 3} \mid \text{at least 2}) = \dfrac{4}{11}\).
Important Questions from Probability of Random Experiments
A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is
A coin is biased so that a head is twice as likely to occur as a tail, if the coin is tossed three times, what is the probability of getting exactly two tails?
From two well shuffled pack of cards what is the probability of getting one Jack from the first one and a King from the second?
If A is an event of getting 13 by throwing two unbiased six-faced dice, then A is called
One summer, Peter visits 4 villages (A, B, C and D) in a random order. Find the probability that he visits (i) A before B (ii) A before B and B before C respectively?
