Question

1. Imagine that you were to shoot a basketball 10 times and you wanted to record the number of shots made.

A.) List an example of an event. (An event is any collection of results/outcomes of a procedure)

B.) List an example of a sample space. (A sample space is a procedure consisting of all simple events)

**I tried this one on my own already but I wanted additional help to see if I was doing this correctly and had the right answer.

5. If I rolled a 4 sided die followed by flipping a coin, what is the probability that I roll an even number followed by getting heads?

6. If the probability of Mr. Hansen makes a three point shot is 10%, what is the probability that Mr. Hansen misses two three point shots in a row?

**Both 5 and 6 events are independent

7. If an event A is making at least one basketball shot, what is the A^c?(A compliment)

**I have the hardest time on probability problems similar to 5 and 6, so please explain along with the answer. Thank you in advance!

Answer 1

.(1) Imagine that you were to shoot a basketball 10 times and you wanted to record the number of shots made.

Here we can have 11 possible options 0 -11, where we can go from making no shots upto making 10.

A.) List an example of an event. (An event is any collection of results/outcomes of a procedure)

We can say that

A; event that we make even number of shots

A = {0, 2, 4, 6, 8, 10} n(A) = 6

Here some of the possible outcomes are present. An event can have zero outcomes (impossible), some outcomes,enitre sample space but not more than sample space.

B.) List an example of a sample space. (A sample space is a procedure consisting of all simple events)

B: Event of getting points in 10 shots

B= {0, 1, 2, 3, 4,5, 6, 7, 8, 9,10}

If we are getting 10 chances we can not make more than 10 hits but we can lose all shots.

**I tried this one on my own already but I wanted additional help to see if I was doing this correctly and had the right answer.

5. If I rolled a 4 sided die followed by flipping a coin, what is the probability that I roll an even number followed by getting heads?

4 sided die event is independent (not affected by) of the event of flipping a coin.

Single outcome of die = 1 / 4 ..............Since out of 4 sides any 1 side is equally possible.

Single outcome of coin = 0.5 ............heads or tails are equally likely.

Sample space

Die	Coin	Outcome
1	H	1H
2	H	2H
3	H	3H
4	H	4H
1	T	1T
2	T	2T
3	T	3T
4	T	4T

There are 8 outcomes out of that we want even die and heads

The bold ones are the desired outcomes

There are 2 desired out of 8.

P = 2 / 8

6. If the probability of Mr. Hansen makes a three point shot is 10%, what is the probability that Mr. Hansen misses two three point shots in a row?

P( making the shot) = 10%

Missing the shot is complement of amking the shot

P(missing) = 1 - P(msking)

= 1 - 10%

= 90% = 0.9

We assume that the making or missing shots are independent of the previous tries.

P( missing 2 shots in a row) = P( missing the 1st time) * P(missing the 2nd time)

= 0.9 * 0.9

**Both 5 and 6 events are independent

7. If an event A is making at least one basketball shot, what is the A^c?(A compliment)

To be of complement of an event means that the two events having nothing in common and their union is the result of the sample space.

A is at least one means 1 or more than 1

Therefore complement would be less than 1. Since less than one '0 shots' (shots can't be -ve)

A complement = 0 shots

**I have the hardest time on probability problems similar to 5 and 6, so please explain along with the answer. Thank you in advance!