Questions: A coin is tossed 3 times. Find the probability. a) getting none head c) getting two head b) Getting one head d) getting three head

Solution Steps

To find the probability of getting none head (0 heads) when a coin is tossed 3 times, we use the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

where:

• \( n = 3 \) (number of trials),
• \( x = 0 \) (number of successes, i.e., heads),
• \( p = 0.5 \) (probability of success),
• \( q = 1 - p = 0.5 \) (probability of failure).

Calculating this gives:

\[ P(X = 0) = \binom{3}{0} \cdot (0.5)^0 \cdot (0.5)^{3} = 1 \cdot 1 \cdot 0.125 = 0.125 \]

Thus, the probability of getting none head is \( 0.125 \).

Next, we calculate the probability of getting two heads (2 heads):

\[ P(X = 2) = \binom{3}{2} \cdot (0.5)^2 \cdot (0.5)^{1} \]

Calculating this gives:

\[ P(X = 2) = 3 \cdot (0.25) \cdot (0.5) = 3 \cdot 0.125 = 0.375 \]

Thus, the probability of getting two heads is \( 0.375 \).

Finally, we find the probability of getting one head (1 head):

\[ P(X = 1) = \binom{3}{1} \cdot (0.5)^1 \cdot (0.5)^{2} \]

Calculating this gives:

\[ P(X = 1) = 3 \cdot (0.5) \cdot (0.25) = 3 \cdot 0.125 = 0.375 \]

Thus, the probability of getting one head is \( 0.375 \).

Final Answer