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QuestionFind the probability of picking a vowel first and a consonant second from cards with letters M,A,R,B,L,EM, A, R, B, L, E.

Studdy Solution

STEP 1

Assumptions1. The letters are M, A, R, B, L, and. Each letter is written on a separate card3. The cards are well mixed in the hat4. A card is chosen randomly, returned, and then another card is chosen5. We are looking for the probability of picking a vowel first and a consonant second

STEP 2

First, we need to identify the vowels and consonants in the given set of letters.Vowels A,Consonants M, R, B, L

STEP 3

Next, we calculate the total number of letters, number of vowels, and number of consonants.
Total letters =6Number of vowels =2Number of consonants =The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability of picking a vowel first is(Vowel first)=Number of vowelsTotal letters(\text{Vowel first}) = \frac{\text{Number of vowels}}{\text{Total letters}}5Substitute the values into the formula to calculate the probability.
(Vowel first)=26(\text{Vowel first}) = \frac{2}{6}6implify the fraction to get the probability of picking a vowel first.
(Vowel first)=13(\text{Vowel first}) = \frac{1}{3}7Similarly, the probability of picking a consonant second is(Consonant second)=Number of consonantsTotal letters(\text{Consonant second}) = \frac{\text{Number of consonants}}{\text{Total letters}}8Substitute the values into the formula to calculate the probability.
(Consonant second)=6(\text{Consonant second}) = \frac{}{6}9implify the fraction to get the probability of picking a consonant second.
(Consonant second)=23(\text{Consonant second}) = \frac{2}{3}10The probability of two independent events happening in sequence is the product of their individual probabilities. So, the probability of picking a vowel first and a consonant second is(Vowel first and Consonant second)=(Vowel first)times(Consonant second)(\text{Vowel first and Consonant second}) =(\text{Vowel first}) \\times(\text{Consonant second})11Substitute the values into the formula to calculate the probability.
(Vowel first and Consonant second)=13times23(\text{Vowel first and Consonant second}) = \frac{1}{3} \\times \frac{2}{3}12Calculate the probability.
(Vowel first and Consonant second)=29(\text{Vowel first and Consonant second}) = \frac{2}{9}The probability that you choose a vowel on your first pick and a consonant on your second pick is 29\frac{2}{9}.

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