A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?a)1/4b)3/8c)1/2d)3/4Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Probability of getting exactly three heads

Answer

Probability of getting exactly three heads

Answer

Problem:
A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

Solution:
To find the probability of getting heads exactly 3 times, we need to consider the number of ways we can get 3 heads out of 4 tosses, and divide it by the total number of possible outcomes.

Step 1: Determine the number of ways to get 3 heads
When tossing a coin, there are two possible outcomes: heads or tails. So, for each toss, we have 2 options. In this case, we want to find the number of ways to get 3 heads, which means we need to choose 3 out of the 4 tosses to be heads.

This can be calculated using the combination formula:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items and r is the number of items to be chosen.

In our case, n = 4 (number of tosses) and r = 3 (number of heads).

Using the combination formula, we have:

C(4, 3) = 4! / (3!(4-3)!) = 4! / (3! * 1!) = 4

So, there are 4 ways to get exactly 3 heads.

Step 2: Determine the total number of possible outcomes
When tossing a coin 4 times, each toss has 2 possible outcomes (heads or tails). Therefore, the total number of possible outcomes is 2^4 = 16.

Step 3: Calculate the probability
The probability of an event is given by the formula:

P(event) = Number of favorable outcomes / Total number of possible outcomes

In this case, the number of favorable outcomes is 4 (the number of ways to get exactly 3 heads) and the total number of possible outcomes is 16.

P(3 heads) = 4 / 16 = 1/4

Therefore, the probability of getting heads exactly 3 times when tossing a coin 4 times is 1/4.

Final Answer:
Option A) 1/4

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