The probability that the number of heads is equal to the number showing on the die is .
According to the question
we roll one fair six-sided die, and flip six coins
i.e
The Total Outcomes is the product of the sample spaces for the dice and the coins.
sample spaces for the dice = 6
sample spaces for the coins = 2⁶
S = 6.2⁶
S = 384
Now, The probability is
Therefore, the Favorable Outcomes
Consider the number of ways to get each total of heads from 1 to 6.
= 2⁶-1 (as TTT is excluded )
= 63
The probability that the number of heads is equal to the number showing on the die
As
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Probability(Event) = Favorable Outcomes/Total Outcomes
By substituting the values in the formula
Probability(Event) =
Probability(Event) =
Hence, the probability that the number of heads is equal to the number showing on the die is
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