Question

A fair coin is tossed 20 times. The probability of getting the three or more heads is 0.7870.the probability of getting three or more heads in a
row or three or more tails in a row is 0.9791. What is the probability of getting three or more heads in a row
and three or more tails in a row?

Answer 1

Given:

Tosses of the coin = 20

Probability of getting the three or more heads = 0.7870

Probability of getting three or more heads or tails in a row = 0.9791.

To Find:

Probability of getting three or more heads in a row  and three or more tails in a row

Solution:

Let the event of getting three or more heads in a row in 20 tosses = X

Let the event of getting three or more tails in a row in 20  tosses = Y

Thus,

P( X ) = P( Y ) = 0.7870 and

P( X ∪ Y) = 0.9791.

Using the probability relation

=  P(X ∪ Y) = P(X) + P(Y) − P(XY),

Thus, the desired probability will be -  

P(XY) = 0.7870 + 0.7870 − 0.9791

= 1.574 - 0.9791

= 0.6 ( Approx)

Answer: The desired probability is 0.6

Answer 2

Answer:

Given,

Tosses of the coin = 20

Probability of getting the three or more heads = 0.7870

Probability of getting three or more heads or tails in a row = 0.9791.

To Find:

Probability of getting three or more heads in a row  and three or more tails in a row

Solution:

Let the event of getting three or more heads in a row in 20 tosses = X

Let the event of getting three or more tails in a row in 20  tosses = Y

Thus,

P( X ) = P( Y ) = 0.7870 and

P( X ∪ Y) = 0.9791.

Using the probability relation

=>  P(X ∪ Y) = P(X) + P(Y) − P(XY),

Thus, the desired probability will be -  

=> P(XY) = 0.7870 + 0.7870 − 0.9791

= 1.574 - 0.9791

= 0.6 ( Approx)

Answer: The desired probability is 0.6

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