A coin is tossed 7 times. find the probability of exactly 5 occurrences fo heads?

The total number of possible outcomes is easy — each coin can be either heads or tails. So that is 2 outcomes per coin. If you’re flipping 7 coins, then the total number of outcomes is 2 ^ 7 = 128.

The number of ways that 5 heads can come up is not as easy to calculate. One way is to write them all out. Here are some combinations for example:

H – H – H – H – H – T – T
H – H – H – H – T – H – T
H – H – H – T – H – H – T
H – H – T – H – H – H – T
H – T – H – H – H – H – T
T – H – H – H – H – H – T
etc
etc
etc

If you wrote out all the arrangements, you’d come up with 21 different combinations. But the easier way is to use the combination probability formula:

# combinations = n! / r! (n-r)! = 7! / (5! * 2!) = 5040 / (120 * 2) = 21

n = number of coins, r = number of heads

So the probability is 21 / 128

2/3

Source(s):
maths pro