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The following outcomes occur when three coins are simultaneously tossed 100 times with the corresponding frequencies:

$n o h e a d − 14 t i m e s, o n e h e a d − 38 t i m e s, t w o h e a d s − 36 t i m e s, t h r e e h e a d s − 12 t i m e s$

What is the probability to obtain more heads than tails?

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2225

1025

1225

225

answer is C.

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Detailed Solution

Given that, 3 coins tossed for 100 times.

n o h e a d − 14 t i m e s, o n e h e a d − 38 t i m e s, t w o h e a d s − 36 t i m e s, t h r e e h e a d s − 12 t i m e s

We have to find the probability of getting more heads than tails.
The probability of an event A is given by,

P (A) = Number of favourable outcomes T o t a l number of outcomes

Total number of outcomes, n(S) = 100.
Let

D

be the event for getting more heads than tails.
We can get more heads than tails in case of getting 2 heads or 3 heads.
n(D) = n(getting 2 heads) + n(getting 3 heads)

⇒ n (D) = 36 + 12 ⇒ n (D) = 48

The probability for getting more heads than tails is given by,

P (D) = n (D) n (S) ⇒ P (D) = 48100 ⇒ P (D) = 2450 ⇒ P (D) = 1225

Thus, the probability for getting more heads than tails are

1225

.
Hence, option 3 is the correct option.

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