# Note: Please explain your answers to all questions, what's the sample space? How do youcalculate the size of sample space? What's the event? How do you calculate the size of theevent? The two questions marked with stars are extra credit questions.1 If you toss a coin for 8 times, what is the probability of getting 2 heads and 6 tails, in anyorder? What is the probability of getting 3 heads and 5 tails, in any order? What's the probabilitythat you get more heads than tails?2 Its known that there are 10 faulty light bulbs among a shipment of 100 light bulbs. If thetesting department randomly chooses 5 light bulbs from the shipment to test, what's theprobability that there is at least one faulty light bulb among the 5 chosen to be tested? 3 Two cards are drawn from a deck of 52 cards, with replacement. (This means that one personchooses a card, looks at it, and returns it, and then another person chooses a card, looks at it,and returns it.)Find the probability that:The first card is an ace and the second card is black.Both cards are spades.Neither card has a value from 2,3,4,5At least one card is an ace.e. If the two cards are drawn without replacement (i.e., first card drawn out is not put backbefore drawing second card), find the probabilities of that both cards are spades.

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Step 1

Hello! As you have posted 3 different questions, we are answering the first question. In case you require the unanswered questions also, kindly re-post them as separate questions.

Step 2

1.

The probability of getting 2 heads and 6 tails is 0.1094 and it is calculated below:

From the given information, a coin is tossed 8 times. That is, the outcomes of the test are either tail or head. And the sample size is finite, and outcomes are independent.

Here, the two heads are selected from 8 coins in 8C2 ways. Hence, there are 6 remaining coins. Therefore, the 6 tail coins are selected from remaining 6 coins in 6C6 ways.

Step 3

The probability of getting 3 heads and 5 tails is 0.2188 and it is calculated below:

Here, the three heads are selected from 8 coins in 8C3 ways. Hence, there...

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