Lottery. In Exercises 15–20, refer to the accompanying table, ...

Question

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events

b. Find the probability of getting 3 or more matches.

Table showing probabilities for matching digits in a lottery: 0.656 for 0, 0.292 for 1, 0.049 for 2, 0.004 for 3, 0+ for 4.

Using Probabilities for Significant Events

b. Find the probability of getting 3 or more matches.

Accepted Answer

Welcome back, everyone. In a mobile app security challenge, users must guess a randomly generated 5 digit access code. Each digit can range from 0 to 9, and digits may repeat. The access code is generated randomly. Let the random variable X represent the number of digits guessed correctly in their appropriate positions. The table below shows the probabilities of correctly guessing 0 to 5 digits. Find the probability of getting 3 or more matches. For this problem because we are looking for the probability of getting 3 or more matches. We can basically state that we are calculating p of X being greater than or equal to 3. According to the properties of probabilities, if we're looking for the probability of X being greater than or equal to 3, this is basically the sum between p of X equals 3 because we begin with 3 and P X 4 because we're using or right we are using addition and finally we can also have P X equals 5. So we're going from 3 up to 5 because we're starting with 3. We need at least 3 matches and at most we can have 5, right? So we're adding those 3 probabilities. And now our table provides us with the corresponding probability values. So we have to substitute those in for the probability of 3 we take 0.025. For the probability of 4, we take 0.004 and for the probability of 5 matches we take 0.001. When we add these we probabilities, we end up with 0.030, which is our final answer to this problem. Thank you for watching.

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