a spinner is divided into seven equal parts with letter A-G written on it. what is the probability of getting two consonants if it is spun twice. Show solution

2 vowel, 5 consonants, so

P(c,c) = 5/7 * 5/7

To find the probability of getting two consonants when spinning the spinner twice, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Step 1: Determine the Total Number of Possible Outcomes
The spinner is divided into seven equal parts, with letters A-G written on it. Therefore, the total number of possible outcomes when spinning it twice is 7 * 7 = 49, as each spin has 7 equally likely outcomes.

Step 2: Determine the Number of Favorable Outcomes
Out of the seven letters (A, B, C, D, E, F, G), three are consonants (B, C, and D). Since we need to get two consonants in two spins, we can calculate the number of favorable outcomes by selecting two consonants from the three available consonants (without replacement) and multiplying it by the number of ways the spins can occur.

The number of ways to select two consonants from three is given by the combination formula, denoted as C(n, r), where n is the total number of items and r is the number of items being chosen. In this case, n = 3 (number of consonants) and r = 2 (number of spins).

Therefore, the number of favorable outcomes is C(3, 2) = 3.

Step 3: Calculate the Probability
Finally, we can calculate the probability of getting two consonants when spinning the spinner twice by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 3 / 49

Thus, the probability of getting two consonants when spinning the spinner twice is 3/49.

To find the probability of getting two consonants when spinning the spinner twice, we need to determine two things: the total number of possible outcomes and the number of favorable outcomes.

Let's start by determining the total number of possible outcomes. Since the spinner is divided into seven equal parts with the letters A-G written on it, there are seven possible outcomes for each spin. Therefore, the total number of possible outcomes when spinning the spinner twice is 7 x 7 = 49.

Next, let's find the number of favorable outcomes, i.e., the outcomes where we get two consonants. Out of the seven letters (A, B, C, D, E, F, G) on the spinner, only three letters (B, C, D) are consonants. So, for the first spin, the probability of getting a consonant is 3/7. For the second spin, since we have already removed one consonant from the spinner, there are only two consonants left out of six remaining options. Thus, the probability of getting a consonant on the second spin is 2/6, which simplifies to 1/3.

To find the probability of both events happening (getting two consonants), we multiply the probabilities of each event together: (3/7) * (1/3) = 3/21.

Simplifying 3/21, we get 1/7.

Therefore, the probability of getting two consonants when spinning the spinner twice is 1/7.

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