You can put this solution on YOUR website! I can't directly access and process images, but based on the description of the image you linked (assuming it's the Venn diagram for the tennis club problem), I can help you solve it.
**Tennis Club Problem**
**Information:**
* There are 90 players in the tennis club.
* 23 are juniors (J).
* The rest are seniors (S).
* 34 seniors and 10 juniors are male (M).
* 8 juniors are left-handed (L), 5 of whom are male.
* There are 18 left-handed players in total, 4 of whom are female seniors.
**Task:**
Calculate the probability of various scenarios related to gender, age group, and handedness.
**Solution:**
**i) Venn Diagram Analysis**
Based on the information, populate the Venn diagram as follows:
* **Total:** 90 players
* **Juniors (J):** 23
* **Male Juniors (J ∩ M):** 10
* **Female Juniors (J ∩ M'):** 13
* **Left-handed Juniors (J ∩ L):** 8
* **Left-handed Female Juniors (J ∩ L ∩ M'):** 3
* **Seniors (S):** 67
* **Male Seniors (S ∩ M):** 34
* **Female Seniors (S ∩ M'):** 33
* **Left-handed Seniors (S ∩ L):** 10
* **Left-handed Female Seniors (S ∩ L ∩ M'):** 4
**ii) Probability Calculations**
**(a) Probability that a male player selected at random is left-handed:**
* P(L | M) = (Number of left-handed males) / (Total number of males)
* P(L | M) = (10 + 5) / (10 + 34)
* P(L | M) = 15 / 44
* P(L | M) ≈ 0.3409
**(b) Probability that a left-handed player selected at random is a female junior:**
* P(J ∩ M' | L) = (Number of left-handed female juniors) / (Total number of left-handed players)
* P(J ∩ M' | L) = 3 / 18
* P(J ∩ M' | L) = 1/6
* P(J ∩ M' | L) ≈ 0.1667
**(c) Probability that a player selected at random is either a junior or a female:**
* P(J ∪ M') = P(J) + P(M') - P(J ∩ M')
* P(J) = 23/90
* P(M') = (Number of females) / (Total players) = (13 + 33) / 90 = 46/90
* P(J ∩ M') = (Number of female juniors) / (Total players) = 13/90
* P(J ∪ M') = (23/90) + (46/90) - (13/90)
* P(J ∪ M') = 56/90
* P(J ∪ M') ≈ 0.6222
**(d) Probability that a player selected at random is right-handed:**
* P(L') = 1 - P(L)
* P(L') = 1 - (18/90)
* P(L') = 72/90
* P(L') = 0.8
**(e) Probability that a right-handed player selected at random is not a junior:**
* P(S | L') = (Number of right-handed seniors) / (Total number of right-handed players)
* P(S | L') = (34 + 33) / 72
* P(S | L') = 67/72
* P(S | L') ≈ 0.9306
**(f) Probability that a right-handed female player selected at random is a junior:**
* P(J | L' ∩ M') = (Number of right-handed female juniors) / (Total number of right-handed female players)
* P(J | L' ∩ M') = 13 / 33
* P(J |
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