Question - Probability of Sequential Events
mathprobability of sequential eventspicking a 6 and 5conditional probability calculationsequential probability formula
Solution:
To solve this probability question, we must consider that the events are sequential and assume that, unless stated otherwise, a chosen number is not replaced. The first event is picking a 6 and the second event is picking a 5.The probability of picking a 6 first:There are 8 numbers in total. Only one of these numbers is a 6. So, the probability of picking a 6 is 1 out of 8, or:\[ P(6) = \frac{1}{8} \]Assuming the 6 is not replaced, we now have 7 numbers left.The probability of picking a 5 next:Since one number (the 6) has already been picked and is not being replaced, there are now 7 numbers remaining. Again, only one of these numbers is a 5. So, the probability of picking a 5 next is 1 out of 7, or:\[ P(5) = \frac{1}{7} \]To find the overall probability of both events happening in sequence (picking a 6 and then a 5), you multiply the probabilities of each individual event:\[ P(6 \text{ and then } 5) = P(6) \times P(5) = \frac{1}{8} \times \frac{1}{7} \]\[ P(6 \text{ and then } 5) = \frac{1}{56} \]Therefore, the probability of picking a 6 and then picking a 5 is $$ \frac{1}{56} $$.
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