Two coins are tossed simultaneously 50 times with the following frequencies of different outcomes:

• Outcomes: 2 heads, 1 head, No heads
• Frequency: 13, 26, 11

Find the probability of each outcome. Show that the sum of the probabilities is equal to 1.

To find the probability of each outcome when two coins are tossed, we first need to understand the frequencies of the outcomes given:

• 2 heads: 13 times
• 1 head: 26 times
• No heads: 11 times

The total number of tosses is:

Total tosses = 13 + 26 + 11 = 50

Calculating Probabilities

The probability of each outcome can be calculated using the formula:

Probability = (Frequency of the outcome) / (Total number of tosses)

1. Probability of getting 2 heads

Using the formula:

P(2 heads) = 13 / 50 = 0.26

2. Probability of getting 1 head

Using the formula:

P(1 head) = 26 / 50 = 0.52

3. Probability of getting no heads

Using the formula:

P(No heads) = 11 / 50 = 0.22

Verifying the Total Probability

To ensure that the sum of the probabilities equals 1, we add them together:

P(2 heads) + P(1 head) + P(No heads) = 0.26 + 0.52 + 0.22 = 1.00

This confirms that the sum of the probabilities is indeed equal to 1, validating our calculations.